Lecture 6-8 Information Technology

Information Technologies The crucial ideas are: Complementarity Network externality

Information Technologies; Complementarity Definition: Commodity A complements commodity B if more of commodity A increases the value of an extra unit of commodity B. More software increases the value of a computer. More roads increase the value of a car.

Information Technologies; Network Externality Definition: A commodity has a positive (negative) network externality if the utility to a consumer of that commodity increases (decreases) as more people also consume the commodity. Email gives more utility to any one user if more other people use email. A highway gives less utility to any one user as more people use it (congestion).

Complementarity Information technologies have increased greatly the complementarities between commodities. Computers and operating systems (OS). DVD players and DVD disks. WiFi sites and laptop computers. Cell phones and cell phone towers.

Complementarity How should a firm behave when it produces a commodity that complements another commodity? The problem is: When you make more of your product (commodity A) you increase the value of firm B’s product (commodity B). Can you get for yourself some of gain you create for firm B?

Complementarity An obvious strategy is for firms A and B to cooperate somewhat with each other. Microsoft releases part of its OS to firms making software that runs under its OS. DVD manufacturers agree upon a standard format for their disks.

Complementarity The price of a computer is pC. The price of the OS is pOS. The quantities demanded of computers and the OS depends upon pC + pOS, not just pC or just pOS.

Complementarity The price of a computer is pC. The price of the OS is pOS. The quantities demanded of computers and the OS depends upon pC + pOS, not just pC or just pOS. Suppose the computer and software firms’ marginal production costs are zero. Fixed costs are FC and FOS.

Complementarity Suppose the firms do not collude. The computer firm’s problem is: choose pC to maximize pCD(pC + pOS) – FC. The OS firm’s problem is: choose pOS to maximize pOSD(pC + pOS) – FOS.

Complementarity Suppose the firms do not collude. The computer firm’s problem is: choose pC to maximize pCD(pC + pOS) – FC. The OS firm’s problem is: choose pOS to maximize pOSD(pC + pOS) – FOS. Assume D(pC + pOS) = a – b(pC + pOS).

Complementarity The computer firm’s problem is: choose pC to maximize pC(a – b(pC + pOS)) – FC. The OS firm’s problem is: choose pOS to maximize pOS(a – b(pC + pOS)) – FOS.

Complementarity Choose pC to maximize pC(a – b(pC + pOS)) – FC  pC = (a – bpOS)/2b. (C) Choose pOS to maximize pOS(a – b(pC + pOS)) – FOS  pOS = (a – bpC)/2b. (OS)

Complementarity Choose pC to maximize pC(a – b(pC + pOS)) – FC  pC = (a – bpOS)/2b. (C) Choose pOS to maximize pOS(a – b(pC + pOS)) – FOS  pOS = (a – bpC)/2b. (OS) A NE is a pair (p*C,p*OS) solving (C) and (OS).

Complementarity Choose pC to maximize pC(a – b(pC + pOS)) – FC  pC = (a – bpOS)/2b. (C) Choose pOS to maximize pOS(a – b(pC + pOS)) – FOS  pOS = (a – bpC)/2b. (OS) A NE is a pair (p*C,p*OS) solving (C) and (OS). p*C = p*OS = a/3b.

Complementarity p*C = p*OS = a/3b. When the firms do not cooperate the price of a computer with an OS is p*C + p*OS = 2a/3b and the quantities demanded of computers and OS are q*C + q*OS = a - b×2a/3b = a/3.

Complementarity What if the firms merge? Then the new firm bundles a computer and an operating system and sells the bundle at a price pB. The firm’s problem is to choose pB to maximize pBD(pB) – FB = pB(a – bpB) – FB.

Complementarity What if the firms merge? Then the new firm bundles a computer and an operating system and sells the bundle at a price pB. The firm’s problem is to choose pB to maximize pBD(pB) – FB = pB(a – bpB) – FB. Solution is p*B = a/2b < 2a/3b.

Complementarity When the firms merge (or fully cooperate) the price of a computer and an OS is p*B = a/2b < 2a/3b and the quantity demanded of bundled computers and OS is q*B = a - b×a/2b = a/2 > a/3.

Complementarity When the firms merge (or fully cooperate) the price of a computer and an OS is p*B = a/2b < 2a/3b and the quantity demanded of bundled computers and OS is q*B = a - b×a/2b = a/2 > a/3. The merged firm supplies more computers and OS at a lower price than do the competing firms. Why?

Complementarity The noncooperative firms ignore the external benefit (complementarity) each creates for the other. So each undersupplies the market, causing a higher market price. These externalities are fully internalized in the merged firm, inducing it to supply more computers and OS and thereby cause a lower market price.

Complementarity More typical cooperation consists of contracts between component manufacturers and an assembler of a final product. Examples are: Car components and a car assembler. A computer assembler and manufacturers of CPUs, hard drives, memory chips, etc.

Complementarity Alternatives include: Revenue-sharing. Two firms share the revenue from the final product made up from the two firms’ components. Licensing. Let firms making complements to your product use your technology for a low fee so they make large quantities of complements, thereby increasing the value of your product to consumers.

Information Technologies; Lock-In Strong complementarities or network externalities make switching from one technology to another very costly. This is called lock-in. E.g., In the USA, it is costly to switch from speaking English to speaking French. How do markets operate when there are switching costs or network externalities?

Competition & Switching Costs Producer’s cost per month of providing a network service is c per customer. Customer’s switching cost is s. Producer offers a one month discount, d. Rate of interest is r.

Competition & Switching Costs All producers set the same nondiscounted price of p per month. When is switching producers rational for a customer?

Competition & Switching Costs Consumer’s cost of not switching is

Competition & Switching Costs Consumer’s cost of not switching is Consumer’s cost from switching is

Competition & Switching Costs Consumer’s cost of not switching is Consumer’s cost from switching is Consumer should switch if

Competition & Switching Costs Consumer’s cost of not switching is Consumer’s cost from switching is Consumer should switch if i.e. if

Competition & Switching Costs Consumer should switch if Producer competition will ensure at a market equilibrium that customers are indifferent between switching or not  I.e., the equilibrium value of the discount only just makes it worthwhile for the customer to switch.

Competition & Switching Costs With d = s, the present-value of the producer’s profits is

Competition & Switching Costs At equilibrium the present-value of the producer’s profit is zero. The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost.

Competition & Switching Costs At equilibrium the present-value of the producer’s profit is zero. The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost. If advertising reduces the marginal cost of servicing a consumer by a then

Competition & Switching Costs At equilibrium the present-value of the producer’s profit is zero. The producer’s price is its marginal cost plus a markup that is a fraction of the consumer’s switching cost. If advertising reduces the marginal cost of servicing a consumer by a then

Competition & Network Externalities Individuals 1,…,1000. Each can buy one unit of a good, providing a network externality. Person v values a unit of the good at nv, where n is the number of persons who buy the good.

Competition & Network Externalities Individuals 1,…,1000. Each can buy one unit of a good providing a network externality. Person v values a unit of the good at nv, where n is the number of persons who buy the good. At a price p, what is the quantity demanded of the good?

Competition & Network Externalities If v is the marginal buyer, valuing the good at nv = p, then all buyers v’ > v value the good more, and so buy it. Quantity demanded is n = 1000 - v. So inverse demand is p = n(1000-n).

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve 1000 n

Competition & Network Externalities Suppose all suppliers have the same marginal production cost, c.

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve 1000 n

Competition & Network Externalities What are the market equilibria?

Competition & Network Externalities What are the market equilibria? (a) No buyer buys, no seller supplies. If n = 0, then value nv = 0 for all buyers v, so no buyer buys. If no buyer buys, then no seller supplies.

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve (a) 1000 n

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve (a) n’ 1000 n

Competition & Network Externalities What are the market equilibria? (b) A small number, n’, of buyers buy. small n’  small network externality value n’v good is bought only by buyers with n’v  c; i.e., only large v  v’ = c/n’.

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve (b) (c) (a) n’ n” 1000 n

Competition & Network Externalities What are the market equilibria? (c) A large number, n”, of buyers buy. Large n”  large network externality value n”v good is bought only by buyers with n’v  c; i.e., up to small v  v” = c/n”.

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve (b) (c) (a) n’ n” 1000 n Which equilibrium is likely to occur?

Competition & Network Externalities Suppose the market expands whenever willingness-to-pay exceeds marginal production cost, c.

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve c Supply Curve n’ n” 1000 n Which equilibrium is likely to occur?

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve Unstable c Supply Curve n’ n” 1000 n Which equilibrium is likely to occur?

Competition & Network Externalities Willingness-to-pay p = n(1000-n) Demand Curve Stable c Supply Curve Stable n” 1000 n Which equilibrium is likely to occur?